Buffered Adaptive Radix – a fast, stable sorting algorithm that trades speed for space at runtime when needed

This paper introduces Buffered Adaptive Radix (BARsort) that adds two improvements to the well known right-to-left Radix sorting algorithm (Right Radix or just Radix). The first improvement, the adaptive part, is that the size of the sorting digit is adjusted according to the maximum value of the elements in the array. This makes BARsort somewhat faster than ordinary 8-bit Radix sort (Radix8). The second and most important improvement is that data is transferred back and forth between the original array and a buffer that can be only a percentage of the size of the original array, as opposed to traditional Radix where that second array is the same length as the original array. Even though a buffer size of 100% of the original array is the fastest choice, any percentage larger than 6% gives a good to acceptable performance. This result is also explained analytically. This flexibility in memory requirement is important in programming languages such as Java where the heap size is fixed at load time and the new operator for constructing the extra array can terminate the program if the requested space is not available. BARsort avoids this problem. In this paper the stable BARsort algorithm is compared to the two non-stable algorithms Quicksort and Flashsort and the ordinary Radix8, which is stable. This is done for 14 different distributions of data and n, the length of the array, varying from 50 to 97M. For the standard distribution, uniform 0:n-1, the relative performance of BARsort versus Quicksort, Flashsort and Radix8 is also shown for Sun UltraSparcIIIi, Intel Core Duo 2500T, Intel Pentium IV and AMD Opteron 254 based machines. A model for the observed execution time is also presented, and, finally, BARsort is proposed as a candidate for a general replacement for Quicksort because of its faster performance and its stable sorting quality.